SAT Math Preparation with Hard Questions

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Question 1 :

If r and s are positive, which of the following expressions is equivalent to (r^6/7s^3/7)^-1?

Answer :

Question 2 :

On Monday, Julie received 240 emails. On Tuesday, the number of emails Julie received was p% less than she received on Monday. Which expression represents the number of emails Julie received on Tuesday?

A) 240(1 – p)

B) 240(p – 1)

C) 240(1 - p/100)

D) 240(p/100 - 1)

Answer :

Question 3 :

Circle A has a radius that is 30% longer than the radius of circle B. The area of circle A is k percent greater than the area of the circle B. What is the value of k?

A) 9

B) 30

C) 36

D) 69

Answer :

Question 4 :

On Friday, a bakery produced 700 bagels per hour for the first 3 hours of operation and 300bagels per hour for the remaning 5 hours of operation. If a bagel produced by the bakery on Friday is selected at random, what is the probability the bagel was produced during the first 4 hours of operation?

Answer :

Question 5 :

Answer :

Question 6 :

It is given that 75ⁿ X 15 = 3⁶ X 5^m. Find the value of (m + n), if m and n are positive integers.

A) 5

B) 8

C) 11

D) 16

Answer :

Question 7 :

In triangles LMN and PQR, angles M and Q each have measure 54°, MN = 16 ands QR = 16. Which of the following additional piece of information is sufficient to prove that triangle LMN is congruent to triangle PQR?

A) Angles L and R each have measure 44°

B) Angles N and P each have measure 44°

C) LN = 11 and PR = 11

D) LM = 11 and PQ = 11

Answer :

Question 8 :

M(t) = 400(1.05)^t/3

The function M models the mass, in nanograms, of a particle after t years. Which of the following is the best interpretation of (1.05)^t^/3 in this context?

A) The mass of the particle increases by 5% every 4 months.

B) The mass of the particle increases by 5% every 3 years.

C) The mass of the particle increases by 5 nanograms every 4 months.

D) The mass of the particle increases by 5 nanograms every 3 years.

Answer :

Question 9 :

ax² + 30x – 9 = 0

In the given equation, a is a constant. The equation has no real solutions, if a < k. What is the greatest possible value of k?

Answer :

Question 10 :

Point B lies on line segment AC such that the length of AB is 7 more than twice the length of BC. If the length of AC is 55, what is the length of AB?

Answer :

Question 11 :

If (x - 7)/5 = (x - 4)/3, the value x - 4 is between which of the following pairs of values ?

A) -9 and -4

B) -1 and 1

C) 2 and 5

D) 7 and 11

Answer :

Question 12 :

A circle with a center B(0, 0) is a unit circle on the xy-plane. Point A(1, 0) and C lie on the circle. If the measurement of angle ABC is 975π/60 in radians. What is the x-coordinate of point C?

A) √2/2

B) -√2/2

C) 0

D) √2/3

Answer :

Question 13 :

A handyman charges a flat rate of $218 for the first 3 hours of work and $68 for each additional hour of work. Which equation gives the total amount y, in dollars, that the handyman charges for x hours of work, where x > 3?

A) y = 68x + 218
B) y = 218x + 68
C) y = 68x + 14
D) y = 68x + 422

Answer :

Question 14 :

For a certain circuit P, in watts; current C, in amperes; voltage V, in volts; and resistance R, in ohms, are related as CV³/P = √PR, where P, C, V and R are positive. When R = 34, which equation correctly expresses P in terms of C and V?

A) P = CV³/√34

B) P = CV³/√34P

C) P = ³√(34/C²V⁴)

D) P = ³√(34/C²V⁶)

Answer :

Question 15 :

f(x) = x + 7

g(x) = 5x² - kx + 245

The function f and g are given. In functiong, k is a constant. If f(x) ⋅ g(x) = 5x³ + 1,715, what is the value of k?

Answer :

Question 16 :

A circle is inscribed inside of square ABCD. Segment AC is the diagonal of the square, and its length is 30 cm. What is the radius of the circle in cm?

A) 15√2/2

B) 15

C) 15√2

D) 30

Answer :

Question 17 :

A metal mold in the shape of a rectangular prism has a length of 27 inches, a width of 48 inches, and a height of 180 inches. The equation c = v(d) calculates the cost of filling the metal mold, where c is the total cost in dollars, v is the volume in cubic yards, and d is the cost per cubic yard. If c is equal to $970, what is the value of d in dollars? (Note 1 yard = 36 inches)

Answer :

Question 18 :

The expression x²⁷(x - 7)/3x³ + 7x²⁷/3x³ is equivalent to ⅓x^k, where k is a constant and x > 0. What is the value of k?

A) 3

B) 27/3

C) 25

D) 28

Answer :

Question 19 :

Megan engages in up to 3 types of exercise each week for a total of 14 hours while training for an ironman competition. Megan runs the same number of minutes each week. The equation y = 780 – x – 200 represents the situation where Megan swims for x minutes during a week and bikes for any remaining training time y, in minutes. If this equation is graphed in the xy-plane, which of the following statements is true?

A) During a week when Megan runs for 780 minutes, she bikes for 200 minutes.

B) Each week, Megan swims and bikes for a total of 780 minutes.

C) During a week when Megan doesn’t bike, she swims for 390 minutes.

D) During a week when Megan doesn’t swim, she runs for 260 minutes.

Answer :

Question 20 :

The functions f and g are defined by the equations shown, where a and b are integer constants, a > b and b > 0. If y = f(x) and y = g(x) are graphed in the xy-plane, which of the following equations displays, as a constant or a coefficient, the maximum of the graph of the corresponding function when x ≥ 0.